Title:
On the Security of Key Extraction from Measuring Physical Quantities

Abstract: Key extraction via measuring a physical quantity is a class of information
theoretic key exchange protocols that rely on the physical characteristics of
the communication channel to enable the computation of a shared key by two (or
more) parties that share no prior secret information. The key is supposed to be
information theoretically hidden to an eavesdropper. Despite the recent surge
of research activity in the area, concrete claims about the security of the
protocols typically rely on channel abstractions that are not fully
experimentally substantiated. In this work, we propose a novel methodology for
the {\em experimental} security analysis of these protocols. The crux of our
methodology is a falsifiable channel abstraction that is accompanied by an
efficient experimental approximation algorithm of the {\em conditional
min-entropy} available to the two parties given the view of the eavesdropper.
We focus on the signal strength between two wirelessly communicating
transceivers as the measured quantity and we use an experimental setup to
compute the conditional min-entropy of the channel given the view of the
attacker which we find to be linearly increasing. Armed with this understanding
of the channel, we showcase the methodology by providing a general protocol for
key extraction in this setting that is shown to be secure for a concrete
parameter selection. In this way we provide a first comprehensively analyzed
wireless key extraction protocol that is demonstrably secure against passive
adversaries. Our methodology uses hidden Markov models as the channel model and
a dynamic programming approach to approximate conditional min-entropy but other
possible instantiations of the methodology can be motivated by our work.